Turbine cooling is typically achieved using compressor bleed air. To improve cycle efficiency, it is desirable to reduce the amount of cooling air diverted form the main gas path. One approach is to use multiple-impingement, or re-use of cooling air to achieve additional cooling. For example, U.S. Pat. No. 4,573,865, to Hsia et al. discloses a multiple-impingement cooled turbine shroud having a unitary construction which includes impingement baffles and internal cavities within which a portion of the shroud surface is impinged with cooling air. However, this construction is complex and expensive to manufacture, and not readily adaptable to variations in the impingement cooling characteristics. Improvement is therefore desired.